Question

The graph of the function f(x) = –(x + 6)(x + 2) is shown below.

Answer 1

Question;

1) The function is increasing for all real values of x where

x < –4.

2) The function is increasing for all real values of x where

–6 < x < –2.

3) The function is decreasing for all real values of x where

x < –6 and where x > –2.

4) The function is decreasing for all real values of x where

x < –4.

Answer:

The correct option is;

1) The function is increasing for all real values of x where x < -4

Step-by-step explanation:

From the question we note that the vertex of the open down parabolic function f(x) = -(x+6)(x+2) is (-4, 4) with x intercept at (-2, 0)

Therefore, since the parabola is symmetric about the vertex, the other x intercept is (-6, 0)

The highest point of the function of the open down (turned, upside down) parabola is the vertex (-4, 4), also, a function is said to be increasing when the y value increases as the x value is increased

Points, f(x) values on the left of the vertex of an opened down parabola are increasing and points on the right are decreasing.

Therefore, since coordinates of points on the left of the vertex are that of x < -4, we have

The function is increasing for all real values of x where x < -4

Answer 2

Answer:

a. The function is increasing for all real values of x where  x < –4.

Step-by-step explanation:

Let me help you, I have answered this question once in Brainly as well

Given the factored form of the function:

f(x) = -(x + 6)(x+2)

<=> f(x) = $-x^{2} - 8x -12$

We will convert to vertex form

$f(x) = -(x+4)^{2} + 4$

Let analyse other possible answers:

a. The function is increasing for all real values of x where  x < –4.

True, because  the parameter a = - 1 so the graph open down all over its domain

b. The function is increasing for all real values of x where  –6 < x < –2.

Wrong, the function decrease in the interval from –4.< x < -2

c. The function is decreasing for all real values of x where  x < –6 and where x > –2.

Wrong, the function increase in the interval from -6 < x < -4

d. The function is decreasing for all real values of x where  x < –4.

Wrong,  The function is increasing  for all real values of x where  x < –4.